Rangers moved out of the Premier League's bottom three thanks to a 2-0 win over fellow strugglers Burnley last weekend.
And as they prepare to try and continue their upward ascent at Goodison Park on Monday, Martinez has praised the way opposite number Harry Redknapp has turned around the London club's lacklustre start to the campaign.
"They have found a way of playing that suits them. I think Harry Redknapp has found the perfect way of adding balance in the side," Martinez told Everton TV.
"They are out of the bottom three. I think they are a team on the up and we have to be at our best."
Martinez's side have, by contrast, slipped down the table in recent weeks.
Back-to-back one-goal away defeats at Tottenham and Manchester City sandwiched a 1-1 draw at home to Hull City, and Everton's winless run in all competitions was extended to four with a 1-0 loss against Kuban Krasnodar in the UEFA Europa League on Thursday.
"We are playing at home, we're desperate to come back home - the experience at Manchester City was really tough and really sad in many ways," he added.
"Having a home game on Monday night, under the lights at Goodison, is exactly the tonic that we need.
"We know we're facing good opposition in a good moment of form but we are desperate to get back in front of our fans and start celebrating a good Christmas period together."
"Our home form has been excellent, we've had great results, but we need to improve our away record," Redknapp told a pre-match media conference.
"It will be tough against Everton - they're a very good side and Goodison Park is a tough place to go.
"We've got to come up with a winning formula to get a positive result.
"Late goals have done for us recently away from home. We need to get points on the board though sooner rather than later."
The manager added: "A few of the players went out for Sunday lunch. Steven fell over. He's okay. He's recovered. End of story."
Everton are likely to revert to a similar line-up to the one that fell agonisingly short at the Etihad Stadium after Martinez gave a run-out to a host of youth team products in Thursday's Europa League encounter with Krasnodar.
